Download What Do We Know (And Not Know) About Potential Output?

What Do We Know (And Not Know)
About Potential Output?
Susanto Basu and John G. Fernald
Potential output is an important concept in economics. Policymakers often use a one-sector neoclassical model to think about long-run growth, and they often assume that potential output is a
smooth series in the short run—approximated by a medium- or long-run estimate. But in both the
short and the long run, the one-sector model falls short empirically, reflecting the importance of
rapid technological change in producing investment goods; and few, if any, modern macroeconomic
models would imply that, at business cycle frequencies, potential output is a smooth series.
Discussing these points allows the authors to discuss a range of other issues that are less well
understood and where further research could be valuable. (JEL E32, O41, E60)
Federal Reserve Bank of St. Louis Review, July/August 2009, 91(4), pp. 187-213.
T
he concept of potential output plays a
central role in policy discussions. In
the long run, faster growth in potential
output leads to faster growth in actual
output and, for given trends in population and
the workforce, faster growth in income per capita.
In the short run, policymakers need to assess the
degree to which fluctuations in observed output
reflect the economy’s optimal response to shocks,
as opposed to undesirable deviations from the
time-varying optimal path of output.
To keep the discussion manageable, we confine our discussion of potential output to neoclassical growth models with exogenous technical
progress in the short and the long run; we also
focus exclusively on the United States. We make
two main points. First, in both the short and the
long run, rapid technological change in producing
equipment investment goods is important. This
rapid change in the production technology for
investment goods implies that the two-sector
neoclassical model—where one sector produces
investment goods and the other produces consumption goods—provides a better benchmark for
measuring potential output than the one-sector
growth model. Second, in the short run, the measure of potential output that matters for policymakers is likely to fluctuate substantially over
time. Neither macroeconomic theory nor existing
empirical evidence suggests that potential output
is a smooth series. Policymakers, however, often
appear to assume that, even in the short run,
potential output is well approximated by a smooth
trend.1 Our model and empirical work corroborate these two points and provide a framework
to discuss other aspects of what we know, and
do not know, about potential output.
As we begin, clear definitions are important
to our discussion. “Potential output” is often used
1
See, for example, Congressional Budget Office (CBO, 2001 and
2004) and Organisation for Economic Co-operation and
Development (2008).
Susanto Basu is a professor in the department of economics at Boston College, a research associate of the National Bureau of Economic
Research, and a visiting scholar at the Federal Reserve Bank of Boston. John G. Fernald is a vice president and economist at the Federal
Reserve Bank of San Francisco. The authors thank Alessandro Barattieri and Kyle Matoba for outstanding research assistance and Jonas
Fisher and Miles Kimball for helpful discussions and collaboration on related research. They also thank Bart Hobijn, Chad Jones, John
Williams, Rody Manuelli, and conference participants for helpful discussions and comments.
© 2009, The Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the
views of the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced,
published, distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts,
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F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
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Basu and Fernald
to describe related, but logically distinct, concepts.
First, people often mean something akin to a
“forecast” for output and its growth rate in the
longer run (say, 10 years out). We will often refer
to this first concept as a “steady-state measure,”
although a decade-long forecast can also incorporate transition dynamics toward the steady state.2
In the short run, however, a steady-state notion
is less relevant for policymakers who wish to
stabilize output or inflation at high frequencies.
This leads to a second concept, explicit in New
Keynesian dynamic stochastic general equilibrium (DSGE) models: Potential output is the rate
of output the economy would have if there were
no nominal rigidities but all other (real) frictions
and shocks remained unchanged.3 In a flexible
price real business cycle model, where prices
adjust instantaneously, potential output is equivalent to actual, equilibrium output. In contrast to
the first definition of potential output as exclusively a long-term phenomenon, the second meaning defines it as relevant for the short run as well,
when shocks push the economy temporarily away
from steady state.
In New Keynesian models, where prices
and/or wages might adjust slowly toward their
long-run equilibrium values, actual output might
well deviate from the short-term measure of potential output. In many of these models, the “output
gap”—the difference between actual and potential
output—is the key variable in determining the
evolution of inflation. Thus, this second definition
also corresponds to the older Keynesian notion
that potential output is the “maximum production without inflationary pressure” (Okun, 1970,
p. 133)—that is, the level of output at which there
is no pressure for inflation to either increase or
decrease. In most, if not all, macroeconomic
models, the second (flexible price) definition
converges in the long run to the first steady-state
definition.
2
In some models, transition dynamics can be very long-lived. For
example, Jones (2002) interprets the past century as a time when
growth in output per capita was relatively constant at a rate above
steady state.
3
See Woodford (2003) for the theory. Neiss and Nelson (2005) construct an output gap from a small, one-sector DSGE model.
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Yet a third definition considers potential output as the current optimal rate of output. With
distortionary taxes and other market imperfections (such as monopolistic competition), neither
steady-state output nor the flexible price equilibrium level of output needs to be optimal or efficient. Like the first two concepts, this third
meaning is of interest to policymakers who might
seek to improve the efficiency of the economy. 4
(However, decades of research on time inconsistency suggest that such policies should be implemented by fiscal or regulatory authorities, who
can target the imperfections directly, but not by
the central bank, which typically must take these
imperfections as given. See, for example, the
seminal paper by Kydland and Prescott, 1977.)
This article focuses on the first two definitions.
The first part of our article focuses on long-term
growth, which is clearly an issue of great importance for the economy, especially in discussions
of fiscal policy. For example, whether promised
entitlement spending is feasible depends almost
entirely on long-run growth. We show that the predictions of two-sector models lead us to be more
optimistic about the economy’s long-run growth
potential. This part of our article, which corresponds to the first definition of potential output,
will thus be of interest to fiscal policymakers.
The second part of our article, of interest to
monetary policymakers, focuses on a time-varying
measure of potential output—the second usage
above. Potential output plays a central, if often
implicit, role in monetary policy decisions. The
Federal Reserve has a dual mandate to pursue low
and stable inflation and maximum sustainable
employment. “Maximum sustainable employment” is usually interpreted to imply that the
Federal Reserve should strive, subject to its other
mandate, to stabilize the real economy around
its flexible price equilibrium level—which itself
is changing in response to real shocks—to avoid
inefficient fluctuations in employment. In New
Keynesian models, deviations of actual from
potential output put pressure on inflation, so in
4
Justiniano and Primiceri (2008) define “potential output” as this
third measure, with no market imperfections; they use the term
“natural output” to mean our second, flexible-wage/price measure.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Basu and Fernald
the simplest such models, output stabilization
and inflation stabilization go hand in hand.
The first section of this article compares the
steady-state implications of one- and two-sector
neoclassical models with exogenous technological
progress. That is, we focus on the long-run effects
of given trends in technology, rather than trying
to understand the sources of this technological
progress.5 Policymakers must understand the
nature of technological progress to devise policies
to promote long-run growth, but it is beyond the
scope of our article. In the next section, we use
the two-sector model to present a range of possible scenarios for long-term productivity growth
and discuss some of the questions these different
scenarios pose.
We then turn to short-term implications and
ask whether it is plausible to think of potential
output as a smooth process and compare the
implications of a simple one-sector versus twosector model. The subsequent section turns to
the current situation (as of late 2008): How does
short-run potential output growth compare with
its steady-state level? This discussion suggests a
number of additional issues that are unknown or
difficult to quantify. The final section summarizes
our findings and conclusions.
capital deepening explains the former and demographics explains the latter. The assumption that
labor productivity evolves separately from hours
worked is motivated by the observation that labor
productivity has risen dramatically over the past
two centuries, whereas labor supply has changed
by much less.6 Even if productivity growth and
labor supply are related in the long run, as suggested by Elsby and Shapiro (2008) and Jones
(1995), the analysis that follows will capture the
key properties of the endogenous response of
capital deepening to technological change.
A reasonable way to estimate steady-state
labor productivity growth is to estimate underlying technology growth and then use a model to
calculate the implications for capital deepening.
Let hats over a variable represent log changes. As
a matter of identities, we can write output growth,
ŷ, as labor-productivity growth plus growth in
hours worked, ĥ:
(
)
yˆ = yˆ − hˆ + hˆ .
We focus here on full-employment labor
productivity.
Suppose we define growth in total factor
productivity (TFP), or the Solow residual, as
 = yˆ − α kˆ − (1 − α ) ˆl ,
tfp
THE LONG RUN: WHAT SIMPLE
MODEL MATCHES THE DATA?
A common, and fairly sensible, approach for
estimating steady-state output growth is to estimate growth in full-employment labor productivity and then allow for demographics to determine
the evolution of the labor force. This approach
motivates this section’s assessment of steadystate labor productivity growth.
We generally think that, in the long run, different forces explain labor productivity and total
hours worked—technology along with induced
5
Of course, total factor productivity (TFP) can change for reasons
broader than technological change alone; improved institutions,
deregulation, and less distortionary taxes are only some of the
reasons. We believe, however, that long-run trends in TFP in
developed countries like the United States are driven primarily
by technological change. For evidence supporting this view, see
Basu and Fernald (2002).
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
where α is capital’s share of income and 共1 – α 兲
is labor’s share of income. Defining
,
lˆ ≡ hˆ + lq
 is labor “quality” (composition) growth,7
where lq
we can rewrite output per hour growth as follows:
(1)
( yˆ − hˆ ) = tfp + α ( kˆ − lˆ ) + lq.
As an identity, growth in output per hour
worked reflects TFP growth; the contribution of
6
King, Plosser, and Rebelo (1988) suggest a first approximation
should model hours per capita as independent of the level of technology and provide necessary and sufficient conditions on the
utility function for this result to hold. Basu and Kimball (2002)
show that the particular non-separability between consumption
and hours worked that is generally implied by the King-PlosserRebelo utility function helps explain the evolution of consumption
in postwar U.S. data and resolves several consumption puzzles.
7
See footnote 7 on p. 190.
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capital deepening, defined as α 共k̂ – lˆ 兲; and
increases in labor quality. Economic models suggest mappings between fundamentals and the
terms in this identity that are sometimes trivial
and sometimes not.
The One-Sector Model
Perhaps the simplest model that could reasonably be applied to the long-run data is the onesector neoclassical growth model. Technological
progress and labor force growth are exogenous
and capital deepening is endogenous.
We can derive the key implications from the
textbook Solow version of the model. Consider
an aggregate production function Y = K α 共AL兲1– α,
where technology A grows at rate g and labor
input L (which captures both raw hours, H, and
labor quality, LQ—henceforth, we do not generally differentiate between the two) grows at rate n.
Expressing all variables in terms of “effective
labor,” AL, yields
y = kα ,
(2)
where y = Y/AL and k = K/AL.
Capital accumulation takes place according
to the perpetual-inventory formula. If s is the
saving rate, so that sy is investment per effective
worker, then in steady state
sy = ( n + δ + g ) k .
(3)
Because of diminishing returns to capital, the
economy converges to a steady state where y and
k are constant. At that point, investment per effective worker is just enough to offset the effects of
7
Labor quality/composition reflects the mix of hours across workers
with different levels of education, experience, and so forth. For the
purposes of this discussion, which so far has focused on definitions, suppose there were J types of workers with factor shares of
income βj , where
∑ j β j = (1 − α ).
Then a reasonable definition of TFP would be
 = yˆ − α kˆ −
tfp
∑ j β j hˆ j .
Growth accounting as done by the Bureau of Labor Statistics or by
Dale Jorgenson and his collaborators (see, for example, Jorgenson,
Gollop, and Fraumeni, 1987) defines
ˆl =
∑ j β j hˆ j
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hˆ = d ln∑ j H j , and qˆ = ˆl − hˆ .
2009
depreciation, population growth, and technological change on capital per effective worker. In
steady state, the unscaled levels of Y and K grow
at the rate g + n; capital deepening, K/L, grows at
rate g. Labor productivity Y/L (i.e., output per unit
of labor input) also grows at rate g.
From the production function, measured
TFP growth is related to labor-augmenting technology growth by
 = Yˆ − α Kˆ − (1 − α ) Lˆ = (1 − α ) g .
tfp
The model maps directly to equation (1). In
particular, the endogenous contribution of capital
deepening to labor-productivity growth is
 / (1 − α ) .
α g = α ⋅ tfp
Output per unit of labor input grows at rate g,
which equals the sum of standard TFP growth,
共1 – α 兲g, and induced capital deepening, α g.
Table 1 shows how this model performs relative to the data. It uses the multifactor productivity release from the Bureau of Labor Statistics
(BLS), which provides data for TFP growth as
well as capital deepening for the U.S. business
economy. These data are shown in the first two
columns. Note that in the model above, standard
TFP growth reflects technology alone. In practice,
a large segment of the literature suggests reasons
why nontechnological factors might affect measured TFP growth. For example, there are hardto-measure short-run movements in labor effort
and capital’s workweek, which cause measured
(although not actual) TFP to fluctuate in the short
run. Nonconstant returns to scale and markups
also interfere with the mapping from technological change to measured aggregate TFP. But the
deviations between technology and measured TFP
are likely to be more important in the short run
than in the long run, consistent with the findings
of Basu, Fernald, and Kimball (2006) and Basu
et al. (2008). Hence, for these longer-term comparisons, we assume average TFP growth reflects
average technology growth. Column 3 shows the
predictions of the one-sector neoclassical model
for α = 0.32 (the average value in the BLS multifactor dataset).
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Basu and Fernald
Table 1
One-Sector Growth Model Predictions for the U.S. Business Sector
Period
Total TFP
Actual capital
deepening contribution
Predicted capital
deepening contribution
in one-sector model
1948-2007
1.39
0.76
0.65
1948-1973
2.17
0.85
1.02
1973-1995
0.52
0.62
0.25
1995-2007
1.34
0.84
0.63
1995-2000
1.29
1.01
0.61
2000-2007
1.37
0.72
0.65
NOTE: Data for columns 1 and 2 are business sector estimates from the BLS multifactor productivity database (downloaded via Haver
on August 19, 2008). Capital and labor are adjusted for changes in composition. Actual capital deepening is α (k̂ – lˆ ), and predicted
 / (1 − α ) .
capital deepening is α ⋅ tfp
A comparison of columns 2 and 3 shows the
model does not perform particularly well. It
slightly underestimates the contribution of capital
deepening over the entire 1948-2007 period, but
it does a particularly poor job of matching the lowfrequency variation in that contribution. In particular, it somewhat overpredicts capital deepening
for the pre-1973 period but substantially underpredicts for the 1973-95 period. That is, given the
slowdown in TFP growth, the model predicts a
much larger slowdown in the contribution of
capital deepening.8
One way to visualize the problem with the
one-sector model is to observe that the model predicts a constant capital-to-output ratio in steady
state—in contrast to the data. Figure 1 shows the
sharp rise in the business sector capital-to-output
ratio since the mid-1960s.
The Two-Sector Model: A Better Match
A growing literature on investment-specific
technical change suggests an easy fix for this
8
Note that output per unit of quality-adjusted labor is the sum of
TFP plus the capital deepening contribution, which in the business
sector averaged 1.39 + 0.76 = 2.15 percent per year over the full
sample. More commonly, labor productivity is reported as output
per hour worked. Over the sample, labor quality in the BLS multifactor productivity dataset rose 0.36 percent per year, so output
per hour rose 2.51 percent per year.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
failure: Capital deepening does not depend on
overall TFP but on TFP in the investment sector.
A key motivation for this body of literature is the
price of business investment goods, especially
equipment and software, relative to the price of
other goods (such as consumption). The relative
price of investment and its main components are
shown in Figure 2.
Why do we see this steady relative price
decline? The most natural interpretation is that
there is a more rapid pace of technological change
in producing investment goods (especially hightech equipment).9
To realize the implications of a two-sector
model, consider a simple two-sector Solow-type
model, where s is the share of nominal output that
is invested each period.10 One sector produces
investment goods, I, that are used to create capital;
the other sector produces consumption goods, C.
The two sectors use the same Cobb-Douglas production function but with potentially different
technology levels:
9
On the growth accounting side, see, for example, Jorgenson (2001)
or Oliner and Sichel (2000); see also Greenwood, Hercowitz, and
Krusell (1997).
10
This model is a fixed–saving rate version of the two-sector neoclassical growth model in Whelan (2003) and is isomorphic to
the one in Greenwood, Hercowitz, and Krusell (1997), who choose
a different normalization of the two technology shocks in their
model.
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Basu and Fernald
Figure 1
Capital-to-Output Ratio in the United States (equipment and structures)
Ratio Scale Index, 1948 = 1
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
1.0
1950
1960
1970
1980
1990
2000
SOURCE: BLS multisector productivity database. Equipment and structures (i.e., fixed reproducible tangible capital) is calculated as a
Tornquist index of the two categories. Standard Industrial Classification data (from www.bls.gov/mfp/historicalsic.htm) are spliced to
North American Industry Classification System data (from www.bls.gov/mfp/mprdload.htm) starting at 1988 (data downloaded
October 13, 2008).
1−α
I = K Iα ( AI LI )
1−α
C = QK Cα ( AI LC )
.
In the consumption equation, we have implicitly defined labor-augmenting technological change
as AC = Q1/共1–α 兲AI to decompose consumption
technology into the product of investment technology, AI , and a “consumption-specific” piece,
Q1/共1–α 兲. Let investment technology, AI , grow at
rate gI and the consumption-specific piece, Q,
grow at rate q. Perfect competition and cost minimization imply that price equals marginal cost.
If the sectors face the same factor prices (and the
same rate of indirect business taxes), then
C
PI
MC
=
= Q.
PC MC I
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The sectors also choose to produce with the same
capital-to-labor ratios, implying that KI /AI LI =
KC /AI LC = K /AI L. We can then write the production functions as
α
I = AI LI ( K AI L )
α
C = QAI LC ( K AI L ) .
We can now write the economy’s budget constraint in a simple manner:
α
Y Inv. Units ; [ I + C Q ] = AI (LI + LC )( K AI L ) ,
(4) or y Inv. Units = k α , where
y Inv. Units = Y Inv. Units AI L and k = K AI L .
“Output” here is expressed in investment
units, and “effective labor” is in terms of technology in the investment sector. The economy
mechanically invests a share s of nominal investF E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Basu and Fernald
Figure 2
Price of Business Fixed Investment Relative to Other Goods and Services
Ratio Scale, 2000 = 100
200
190
180
170
160
Equipment and Software
150
140
Business Fixed Investment
130
120
110
100
90
80
Structures
1960
1965
1970 1975 1980
1985
1990
1995
2000
2005
NOTE: “Other goods and services” constitutes business GDP less business fixed investment.
SOURCE: Bureau of Economic Analysis and authors’ calculations.
ment, which implies that investment per effective
unit of labor is i = s . y Inv. Units.11 Capital accumulation then takes the same form as in the one-sector
model, except that it is only growth in investment
technology, gI, that matters. In particular, in steady
state,
(5)
sy Inv. Units = ( n + δ + g I ) k .
The production function (4) and capitalaccumulation equation (5) correspond exactly to
their one-sector counterparts. Hence, the dynamics
of capital in this model reflect technology in the
investment sector alone. In steady state, capital per
unit of labor, K/L, grows at rate gI , so the contribution of capital deepening to labor-productivity
growth from equation (1) is
11
s ⋅ y Inv. Units =  PI I ( PI I + PC C )  ( I + PC C PI ) AI L  = I AI L .
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
 (1 − α ) .
α g I = α ⋅ tfp
I
Consumption technology in this model is “neutral” in that it does not affect investment or capital
accumulation; the same result carries over to the
Ramsey version of this model, with or without
variable labor supply. (Basu et al., 2008, discuss
the idea of consumption-technology neutrality
in greater detail.12)
To apply this model to the data, we need to
decompose aggregate TFP growth (calculated from
12
Note also that output in investment units is not equal to chain output in the national accounts. Chain gross domestic product (GDP) is
Yˆ = sIˆ + (1 − s )Cˆ .

Inv. Units
In contrast, in this model Y
= sIˆ + (1 − s ) Cˆ − (1 − s ) q.

Inv. Units
Hence, Ŷ = Y
+ (1 − s )q .
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Basu and Fernald
chained output) into its consumption and investment components. Given the conditions so far,
the following two equations hold:
 = s ⋅ tfp
 + ( 1 − s )tfp
 ,
tfp
I
C




P − P = tfp − tfp .
C
I
C
I
These are two equations in two unknowns—
 and tfp
 .
tfp
I
C
Hence, they allow us to decompose aggregate TFP
growth into investment and consumption TFP
growth.13
Table 2 shows that the two-sector growth
model does, in fact, fit the data better. All derivations are done assuming an investment share of
0.15, about equal to the nominal value of business
fixed investment relative to the value of business
output.
For the 1948-73 and 1973-95 periods, a comparison of columns 5 and 6 indicates that the
model fits quite well—and much better than the
one-sector model. The improved fit reflects that
although overall TFP growth slowed very sharply,
investment TFP growth (column 3) slowed much
less. Hence, the slowdown in capital deepening
was much smaller.
The steady-state predictions work less well
for the periods after 1995, when actual capital
deepening fell short of the steady-state prediction
for capital deepening. During these periods, not
only did overall TFP accelerate, but the relative
price decline in column 2 also accelerated. Hence,
implied investment TFP accelerated markedly (as
did other TFP). Of course, the transition dynamics imply that capital deepening converges only
slowly to the new steady state, and a decade is a
relatively short time. (In addition, the pace of
investment-sector TFP was particularly rapid in
the late 1990s and has slowed somewhat in the
2000s.) So the more important point is that, quali13
The calculations below use the official price deflators from the
national accounts. Gordon (1990) argues that many equipment
deflators are not sufficiently adjusted for quality improvements
over time. Much of the macroeconomic literature since then has
used the Gordon deflators (possibly extrapolated, as in Cummins
and Violante, 2002). Of course, as Whelan (2003) points out, much
of the discussion of biases in the consumer price index involves
service prices, which also miss many quality improvements.
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2009
tatively, the model works in the right direction
even over this relatively short period.
Despite these uncertainties, a bottom-line
comparison of the one- and two-sector models is
of interest. Suppose that the 1995-2007 rates of
TFP growth continue to hold in both sectors (a big
“if” discussed in the next section). Suppose also
that the two-sector model fits well going forward,
as it did in the 1948-95 period. Then we would
project that future output per hour (like output
per quality-adjusted unit of labor, shown in
Tables 1 and 2) will grow on average about 0.75
percentage points per year faster than the onesector model would predict (1.38 versus 0.63), as
a result of greater capital deepening. The difference is clearly substantial: It is a significant fraction of the average 2.15 percent growth rate in
output per unit of labor (and 2.5 percent growth
rate of output per hour) over the 1948-2007 period.
PROJECTING THE FUTURE
Forecasters, policymakers, and a number of
academics regularly make “structured guesses”
about the likely path of future growth.14 Not surprisingly, the usual approach is to assume that
the future will look something like the past—but
the challenge is to decide which parts of the past
to include and which to downplay.
In making such predictions, economists often
project average TFP growth for the economy as a
whole. However, viewed through the lens of the
two-sector model, one needs to make separate
projections for TFP growth in both the investment and non-investment sectors. We consider
three growth scenarios: low, medium, and high
(Table 3).
Consider the medium scenario, which has
output per hour growing at 2.3 (last column).
Investment TFP is a bit slower than its average
in the post-2000 period, reflecting that investment TFP has generally slowed since the burst
of the late 1990s. Other TFP slows to its rate in
14
Oliner and Sichel (2002) use the phrase “structured guesses.” In
addition to Oliner and Sichel, recent high-profile examples of
projections have come from Jorgenson, Ho, and Stiroh (2008) and
Gordon (2006). The CBO and the Council of Economic Advisers
regularly include longer-run projections of potential output.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
2.17
0.52
1.34
1.29
1.37
0.21
0.98
1948-1973
1973-1995
1995-2007
1995-2000
2000-2007
2004:Q4–2006:Q4
2006:Q4–2008:Q3
–1.12
0.29
–1.17
–2.93
–1.90
–1.02
0.33
–0.61
1.94
–0.04
2.36
3.78
2.94
1.39
1.89
1.91
0.82
0.25
1.20
0.85
1.04
0.37
2.22
1.29
Other TFP
—
—
0.72
1.01
0.84
0.62
0.85
0.76
Actual
capital deepening
contribution
—
—
1.11
1.78
1.38
0.66
0.89
0.90
Predicted
capital deepening
contribution
in two-sector model
SOURCE: BLS multifactor productivity dataset, Bureau of Economic Analysis relative-price data, and authors’ calculations. The final two rows reflect quarterly estimates
from Fernald (2008); because of the very short sample periods, we do not show steady-state predictions.
NOTE: “Other goods and services” constitutes business GDP less business fixed investment. Capital and labor are adjusted for changes in composition. Actual capital deep / (1 − α ) .
ening is α (k̂ – lˆ ), and predicted capital deepening is α ⋅ tfp
1.39
Total TFP
1948-2007
Period
Relative price of
business fixed investment
to other
goods and services Investment TFP
Two-Sector Growth Model Predictions for the U.S. Business Sector
Table 2
Basu and Fernald
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Table 3
A Range of Estimates for Steady-State Labor Productivity Growth
Growth scenario
Investment TFP
Other TFP
Overall TFP
Capital
deepening
contribution
Labor
productivity
Output per
hour worked
Low
1.00
0.70
0.7
0.5
1.2
1.5
Medium
2.00
0.82
1.0
0.9
2.0
2.3
High
2.50
1.10
1.3
1.2
2.5
2.8
NOTE: Calculations assume an investment share of output of 0.15 and a capital share in production, α , of 0.32. Column 3 (Overall TFP)
is an output-share-weighted average of columns 1 and 2. Column 4 is column 1 multiplied by α /(1 – α ). Column 5 is output per unit
of composition-adjusted labor input and is the sum of columns 3 and 4. Column 6 adds an assumed growth rate of labor quality/
composition of 0.3 percent per year, and therefore equals column 5 plus 0.3 percent.
the second half of the 1990s, reflecting an assumption that the experience of the early 2000s is
unlikely to persist.
Productivity growth averaging about 2.25 percent is close to a consensus forecast. For example,
in the first quarter of 2008, the median estimate
in the Survey of Professional Forecasters (SPF,
2008) was for 2 percent labor-productivity growth
over the next 10 years (and 2.75 percent gross
domestic product [GDP] growth). In September
2008, the Congressional Budget Office estimated
that labor productivity (in the nonfarm business
sector) would grow at an average rate of about
2.2 percent between 2008 and 2018.15
As Table 3 clearly shows, however, small and
plausible changes in assumptions—well within
the range of recent experience—can make a large
difference for steady-state growth projections.
As a result, a wide range of plausible outcomes
exists. In the SPF, the standard deviation across
the 39 respondents for productivity growth over
the next 10 years was about 0.4 percent—with a
range of 0.9 to 3.0 percent. Indeed, the current
median estimate of 2.0 percent is down from an
estimate of 2.5 percent in 2005, but remains much
higher than the one-year estimate of only 1.3 percent in 1997.16
15
Calculated from data in CBO (2008).
16
The SPF has been asking about long-run projections in the first
quarter of each year since 1992. The data are available at
www.philadelphiafed.org/research-and-data/real-time-center/
survey-of-professional-forecasters/data-files/PROD10/.
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The two-sector model suggests several key
questions in making long-run projections. First,
what will be the pace of technical progress in
producing information technology (IT) and, more
broadly, equipment goods? For example, for hardware, Moore’s law—that semiconductor capacity
doubles approximately every two years—provides
plausible bounds. For software, however, we really
have very little firm ground for speculation.
Second, how elastic is the demand for IT?
The previous discussion of the two-sector model
assumed that the investment share was constant
at 0.15. But an important part of the price decline
reflected that IT, for which prices have been falling
rapidly, is becoming an increasing share of total
business fixed investment. At some point, a constant share is a reasonable assumption and consistent with a balanced growth path. Yet over the
next few decades, very different paths are possible.
Technology optimists (such as DeLong, 2002)
think that the elasticity of demand for IT exceeds
unity, so that demand will rise even faster than
prices fall. They think that firms and individuals
will find many new uses for computers, semiconductors, and, indeed, information, as these
commodities get cheaper and cheaper. By contrast,
technology pessimists (such as Gordon, 2000)
think that the greatest contribution of the IT revolution is in the past rather than the future. For
example, firms may decide they will not need
much more computing power in the future, so
that as prices continue to fall, the nominal share
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Basu and Fernald
of expenditure on IT will also fall. For example,
new and faster computers might offer few advantages for word processing relative to existing computers, so the replacement cycle might become
longer.
Third, what will happen to TFP in the non-ITproducing sectors? The range of uncertainty here
is very large—larger, arguably, than for the first
two questions. The general-purpose-technology
nature of computing suggests that faster computers and better ability to manage and manipulate
information might well lead to TFP improvements
in computer-using sectors.17 For example, many
important management innovations, such as the
Wal-Mart business model or the widespread diffusion of warehouse automation, are made possible by cheap computing power. Productivity in
research and development may also rise more
directly; auto parts manufacturers, for example,
can design new products on a computer rather
than building physical prototype models. That
is, computers may lower the cost and raise the
returns to research and development
In addition, are these sorts of TFP spillovers
from IT to non-IT sectors best considered as
growth effects or level effects? For example, the
“Wal-Martization” of retailing raises productivity
levels (as more-efficient producers expand and
less-efficient producers contract) but it does not
necessarily boost long-run growth.
Fourth, the effects noted previously might
well depend on labor market skills. Many endogenous growth models incorporate a key role for
human capital, which is surely a key input into
the innovation process—whether reflected in
formal research and development or in management reorganizations. Beaudry, Doms, and Lewis
(2006) find evidence that the intensity of personal
computers use across U.S. cities is closely related
to education levels in those cities.
We hope we have convinced readers that it is
important to take a two-sector approach to esti17
See, for example, Basu et al. (2003) for an interpretation of the
broad-based TFP acceleration in terms of intangible organizational
capital associated with using computers. Of course, an intangiblecapital story suggests that the measured share of capital is too low,
and that measured capital is only a subset of all capital—so the
model and calibration in the earlier section are incomplete.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
mating the time path of long-run output. But as
this (non-exhaustive) discussion demonstrates,
knowing the correct framework for analysis is only
one of many inputs to projecting potential output
correctly. Much still remains unknown about
potential output, even along a steady-state growth
path. The biggest problem is the lack of knowledge about the deep sources of TFP growth.
SHORT-RUN CONSIDERATIONS
General Issues in Defining and
Estimating Short-Run Potential Output
Traditionally, macroeconomists have taken
the view expressed in Solow (1997) that, in the
long-run, a growth model such as the ones
described previously explains the economy’s
long-run behavior. Factor supplies and technology
determine output, with little role for “demand”
shocks. However, the short run was viewed very
differently, when as Solow (1997) put it, “…fluctuations are predominantly driven by aggregate
demand impulses” (p. 230).
Solow (1997) recognizes that real business
cycle theories take a different view, providing a
more unified vision of long-run growth and shortrun fluctuations than traditional Keynesian views
did. Early real business cycle models, in particular,
emphasized the role of high-frequency technology
shocks. These models are also capable of generating fluctuations in response to nontechnological
“demand” shocks, such as government spending.
Since early real business cycle models typically
do not incorporate distortions, they provide examples in which fluctuations driven by government
spending or other impulses could well be optimal
(taking the shocks themselves as given). Nevertheless, traditional Keynesian analyses often presumed that potential output was a smooth trend,
so that any fluctuations were necessarily suboptimal (regardless of whether policy could do anything about them).
Fully specified New Keynesian models provide a way to think formally about the sources of
business cycle fluctuations. These models are
generally founded on a real business cycle model,
albeit one with real distortions, such as firms
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having monopoly power. Because of sticky wages
and/or prices, purely nominal shocks, such as
monetary policy shocks, can affect real outcomes.
The nominal rigidities also affect how the economy responds to real shocks, whether to technology, preferences, or government spending.
Short-run potential output is naturally defined
as the rate of output the economy would have if
there were no nominal rigidities, that is, by the
responses in the real business cycle model
underlying the sticky price model.18 This is our
approach to producing a time series of potential
output fluctuations in the short run.
In New Keynesian models, where prices
and/or wages might adjust slowly toward their
long-run equilibrium values, actual output might
well deviate from this short-term measure of potential output. In many of these models, the “output
gap”—the difference between actual and potential
output—is the key variable in determining the
evolution of inflation. Kuttner (1994) and Laubach
and Williams (2003) use this intuition to estimate
the output gap as an unobserved component in a
Phillips curve relationship. They find fairly substantial time variation in potential output.
In the context of New Keynesian DSGE models,
is there any reason to think that potential output
is a smooth series? At a minimum, a low variance
of aggregate technology shocks as well as inelastic
labor supply is needed. Rotemberg (2002), for
example, suggests that because of slow diffusion
of technology across producers, stochastic technological improvements might drive long-run
growth without being an important factor at business cycle frequencies.19
18
See Woodford (2003). There is a subtle issue in defining flexible
price potential output when the time path of actual output may be
influenced by nominal rigidities. In theory, the flexible price output series should be a purely forward-looking construct, which is
generated by “turning off” all nominal rigidities in the model, but
starting from current values of all state variables, including the
capital stock. Of course, the current value of the capital stock might
be different from what it would have been in a flexible price model
with the same history of shocks because nominal rigidities operated
in the past. Thus, in principle, the potential-output series should
be generated by initializing a flexible price model every period,
rather than taking an alternative time-series history from the flexible
price model hit by the same sequence of real shocks. We do the
latter rather than the former because we believe that nominal rigidities cause only small deviations in the capital stock, but it is possible that the resulting error in our potential-output series might
actually be important.
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Nevertheless, although a priori one might
believe that technology changes only smoothly
over time, there is scant evidence to support this
position. Basu, Fernald, and Kimball (2006) control econometrically for nontechnological factors
affecting the Solow residual—nonconstant returns
to scale, variations in labor effort and capital’s
workweek, and various reallocation effects—and
still find a “purified technology” residual that is
highly variable. Alexopoulos (2006) uses publications of technical books as a proxy for unobserved
technical change and finds that this series is not
only highly volatile, but explains a substantial
fraction of GDP and TFP. Finally, variance decompositions often suggest that innovations to technology explain a substantial share of the variance
of output and inputs at business cycle frequencies;
see Basu, Fernald, and Kimball (2006) and Fisher
(2006).
When producing a time series of short-run
potential output, it is necessary not only to know
“the” correct model of the economy, but also the
series of historical shocks that have affected the
economy. One approach is to specify a model,
which is often complex, and then use Bayesian
methods to estimate the model parameters on
the data. As a by-product, the model estimates
the time series of all the shocks that the model
allows.20 Because DSGE models are “structural”
in the sense of Lucas’s (1976) critique, one can
perform counterfactual simulations—for example, by turning off nominal rigidities and using
the estimated model and shocks to create a time
series of flexible price potential output.
We do not use this approach because we are
not sure that Bayesian estimation of DSGE models
always uses reliable schemes to identify the relevant shocks. The full-information approach of
these models is, of course, preferable in an efficiency sense—if one is sure that one has specified
19
A recent paper by Justiniano and Primiceri (2008) estimates both
simple and complex New Keynesian models and finds that most
of the volatility in the flexible-wage/price economy reflects extreme
volatility in markup shocks. They still estimate that there is considerable quarter-to-quarter volatility in technology, so that even
if the only shocks were technology shocks, their flexible price
measure of output would also have considerable volatility from
one quarter to the next.
20
See Smets and Wouters (2007).
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Basu and Fernald
the correct structural model of the economy
with all its frictions. We prefer to use limitedinformation methods to estimate the key shocks—
technology shocks, in our case—and then feed
them into small, plausibly calibrated models of
fluctuations. At worst, our method should provide
a robust, albeit inefficient, method of assessing
some of the key findings of DSGE models estimated using Bayesian methods.
We believe that our method of estimating the
key shocks is both more transparent in its identification and robust in its method because it does
not rely on specifying correctly the full model of
the economy, but only small pieces of such a
model. As in the case of the Basu, Fernald, and
Kimball (2006) procedure underlying our shock
series, we specify only production functions and
costs of varying factor utilization and assume that
firms minimize costs—all standard elements of
current “medium-scale” DSGE models. Furthermore, we assume that true technology shocks
are orthogonal to other structural shocks, such
as monetary policy shocks, which can therefore
be used as instruments for estimation. Finally,
because we do not have the overhead of specifying and estimating a complete structural general
equilibrium model, we are able to model the
production side of the economy in greater detail.
Rather than assuming that an aggregate production function exists, we estimate industry-level
production functions and aggregate technology
shocks from these more disaggregated estimates.
Basu and Fernald (1997) argue that this approach
is preferable in principle and solves a number of
puzzles in recent production-function estimation
in practice.
We use time series of “purified” technology
shocks, similar to those presented in Basu,
Fernald, and Kimball (2006) and Basu et al. (2008).
However, these series are at an annual frequency.
Fernald (2008) applies the methods in these
articles to quarterly data and produces higherfrequency estimates of technology shocks. Fernald
estimates utilization-adjusted measures of TFP for
the aggregate economy, as well as for the investment and consumption sector. In brief, aggregate
TFP is measured using data from the BLS quarterly
labor productivity data, combined with capitalF E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
service data estimated from detailed quarterly
investment data. Labor quality and factor shares
are interpolated from the BLS multifactorproductivity dataset. The relative price of investment goods is used to decompose aggregate TFP
into investment and consumption components,
using the (often-used) assumption that relative
prices reflect relative TFPs. The utilization adjustment follows Basu, Fernald, and Kimball (2006),
who use hours per worker as a proxy for utilization change (with an econometrically estimated
coefficient) at an industry level. The input-output
matrix was used to aggregate industry utilization
change into investment and consumption utilization change, following Basu et al. (2008).21
To produce our estimated potential output
series, we feed the technology shocks estimated
by Fernald (2008) into simple one- and two-sector
models of fluctuations (see the appendix). Technology shocks shift the production function
directly, even if they are not amplified by changes
in labor supply in response to variations in wages
and interest rates. If labor supply is elastic, then
a fortiori the changes in potential output will be
more variable for any given series of technology
shocks.
Elastic labor supply also allows nontechnology
shocks to move short-run, flexible price output
discontinuously. Shocks to government spending,
even if financed by lump-sum taxes, cause changes
in labor supply via a wealth effect. Shocks to distortionary tax rates on labor income shift labor
demand and generally cause labor input, and
hence output, to change. Shocks to the preference
for consumption relative to leisure can also cause
changes in output and its components.
The importance of all of these shocks for
movements in flexible price potential output
depends crucially on the size of the Frisch
(wealth-constant) elasticity of labor supply.
Unfortunately, this is one of the parameters in
economics whose value is most controversial, at
least at an aggregate level. Most macroeconomists
assume values between 1 and 4 for this crucial
21
Because of a lack of data at a quarterly frequency, Fernald (2008)
does not correct for deviations from constant returns or for heterogeneity across industries in returns to scale—issues that Basu,
Fernald, and Kimball (2006) argue are important.
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parameter, but not for particularly strong reasons.22 On the other hand, Card (1994) reviews
both microeconomic and aggregative evidence
and concludes there is little evidence in favor of
a nonzero Frisch elasticity of labor supply. The
canonical models of Hansen (1985) and Rogerson
(1988) attempt to bridge the macro-micro divide.
However, Mulligan (2001) argues that the strong
implication of these models, an infinite aggregate
labor supply elasticity, depends crucially on the
assumption that workers are homogeneous and
can easily disappear when one allows for heterogeneity in worker preferences.
We do not model real, nontechnological
shocks to the economy in creating our series on
potential output. Our decision is partly due to
uncertainty over the correct value of the aggregate
Frisch labor supply elasticity, which as discussed
previously is crucial for calibrating the importance of such shocks. We also make this decision
because in our judgment there is even less consensus in the literature over identifying true innovations to fiscal policy or to preferences than there
is on identifying technology shocks. Our decision
to ignore nontechnological real shocks clearly
has the potential to bias our series on potential
output, and depending on the values of key parameters, this bias could be significant.
One-Sector versus Two-Sector Models
In the canonical New Keynesian Phillips
curve, derived with Calvo price setting and flexible wages, inflation today depends on expected
inflation tomorrow, as well as on the gap between
actual output and the level of output that would
occur with flexible prices.
To assess how potential and actual output
respond in the short run in a one- versus twosector model, we used a very simple two-sector
New Keynesian model (see the appendix). As in
the long-run model, we assume that investment
22
In many cases, it is simply because macro models do not “work”—
that is, display sufficient amplification of shocks—for smaller
values of the Frisch labor supply elasticity. In other cases, values
like 4 are rationalized by assuming, without independent evidence,
that the representative consumer’s utility from leisure takes the
logarithmic form. However, this restriction is not imposed by the
King-Plosser-Rebelo (1988) utility function, which guarantees
balanced growth for any value of the Frisch elasticity.
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and consumption production uses a Cobb-Douglas
technology with the same factor shares but with
a (potentially) different multiplicative technology
parameter. To keep things simple, factors are
completely mobile, so that a one-sector model is
the special case when the same technology shock
hits both sectors.
We simulated the one- and two-sector models
using the utilization-adjusted technology shocks
estimated in Fernald (2008). Table 4 shows standard deviations of selected variables in flexible
and sticky price versions of the one- and twosector models, along with actual data for the U.S.
economy.
The model does a reasonable job of approximating the variation in actual data, considering
how simple it is and that only technology shocks
are included. Investment in the data is slightly
less volatile than either in the sticky price model
or the two-sector flexible price model. This is not
surprising, given that the model does not have any
adjustment costs or other mechanisms to smooth
out investment. Consumption, labor, and output
in the data are more volatile than in the models.23
Additional shocks (e.g., to government spending,
monetary policy, or preferences) would presumably add volatility to model simulations.
An important observation from Table 4 is that
potential output—the flexible price simulations,
in either the one- or two-sector variants—is highly
variable, roughly as variable as sticky price output. The short-run variability of potential output
in New Keynesian models has been emphasized
by Neiss and Nelson (2005) and Edge, Kiley, and
Laforte (2007).
These models, with the shocks we have added,
show a very high correlation of flexible and sticky
price output. In the two-sector case, the correlation is 0.91. Nevertheless, the implied output gap
(shown in the penultimate line of Table 4 as the
difference between output in the flexible and
sticky price cases) is more volatile than would be
implied if potential output were estimated with
the one-sector model (the final line).
23
The relative volatility of consumption is not that surprising,
because the models do not have consumer durables and we have
not yet analyzed consumption of nondurables and services in the
actual data.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
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Table 4
Standard Deviations, Model Simulations, and Data
Variable
Investment
Consumption
Labor
Output
One-sector, flexible price
4.40
0.81
0.47
1.52
Two-sector, flexible price
6.28
0.89
0.73
1.66
One-sector, sticky price
4.82
0.84
0.64
1.60
Two-sector, sticky price
5.52
0.87
0.85
1.68
Data
4.54
1.12
1.14
1.95
Output gap (two-sector sticky price
less two-sector flexible price)
5.78
0.59
0.96
0.72
“One-sector” estimated gap (two-sector sticky price
less one-sector flexible price)
2.55
0.18
0.59
0.41
NOTE: Model simulations use utilization-adjusted TFP shocks from Fernald (2008). Two-sector simulations use estimated quarterly
consumption and investment technology; one-sector simulations use the same aggregate shock (a share-weighted average of the two
sectoral shocks) in both sectors. All variables are filtered with the Christiano-Fitzgerald bandpass filter to extract variation between 6
and 32 quarters.
Figure 3 shows that the assumption that potential output has no business cycle variation—
which is tantamount to using (Hodrick-Prescott–
filtered) sticky price output itself as a proxy for
the output gap—would overestimate the variation
in the output gap. This would not matter too much
if the output gap were perfectly correlated with
sticky price output itself—then, at least, the sign,
if not the magnitude, would be correct. However,
as the figure shows, the “true” two-sector output
gap in the model (two-sector sticky price output
less two-sector flexible price output) is imperfectly
correlated with sticky price output—indeed, the
correlation is only 0.25. So in this model, policymakers could easily be misled by focusing solely
on output fluctuations rather than the output gap.
Implications for Stabilization Policy
If potential output fluctuates substantially
over time, then this has potential implications
for the desirability of stabilization policy. In particular, policymakers should be focused only on
stabilizing undesirable fluctuations.
Of course, the welfare benefits of such policies
remain controversial. Lucas (1987, 2003) famously
argued that, given the fluctuations we observe,
the welfare gains from additional stabilization of
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
the economy are likely to be small. In particular,
given standard preferences and the observed
variance of consumption (around a linear trend),
a representative consumer would be willing to
reduce his or her average consumption by only
about ½ of 1/10 th of 1 percent in exchange for
eliminating all remaining variability in consumption. Note that this calculation does not necessarily imply that stabilization policy does not
matter, because the calculation takes as given the
stabilization policies implemented in the past.
Stabilization policies might well have been valuable—for example, in eliminating recurrences of
the Great Depression or by minimizing the frequency of severe recessions—but additional stabilization might not offer large benefits.
This calculation amounts to some $5 billion
per year in the United States, or about $16 per
person. Compared with the premiums we pay for
very partial insurance (e.g., for collision coverage
on our cars), this is almost implausibly low. Any
politician would surely vote to pay $5 billion for
a policy that would eliminate recessions.
Hence, a sizable literature considers ways to
obtain larger costs of business cycle fluctuations,
with mixed results. Arguments in favor of stabilization include Galí, Gertler, and López-Salido
(2007), who argue that the welfare effects of booms
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Basu and Fernald
Figure 3
Output Gap and Sticky Price Output
Percent
6
4
2
0
–2
–4
Two-Sector Sticky Price Model
Two-Sector Output
:Q
3
07
20
02
20
:Q
3
3
:Q
3
:Q
97
19
3
:Q
92
19
87
19
19
82
:Q
:Q
3
3
3
77
19
:Q
72
19
67
19
:Q
3
3
:Q
3
62
:Q
57
19
:Q
19
52
19
19
4
7:
Q
3
3
–6
NOTE: Bandpass-filtered (6 to 32 quarters) output from two-sector sticky price model and the corresponding output gap (defined as
sticky price output less flexible price output).
and recessions may be asymmetric. In particular,
because of wage and price markups, steady-state
employment and output are inefficiently low
in their model, so that the costs of fluctuations
depend on how far the economy is from full
employment. Recessions are particularly costly—
welfare falls by more during a business cycle
downturn than it rises during a symmetric expansion. Barlevy (2004) argues in an endogenousgrowth framework that stabilization might increase
the economy’s long-run growth rate; this allowed
him to obtain very large welfare effects from business cycle volatility.
This discussion of welfare effects highlights
that much work remains to understand the desirability of observed fluctuations, the ability of
policy to smooth the undesirable fluctuations in
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the output gap, and the welfare benefits of such
policies.
WHAT IS CURRENT POTENTIAL
OUTPUT GROWTH?
Consider the current situation, as of late 2008:
Is potential output growth relatively high, relatively low, or close to its steady-state value?24
The answer is important for policymakers, where
statements by the Federal Open Market Committee
(FOMC) participants have emphasized the impor24
We could, equivalently, discuss the magnitude or even sign of the
output gap, which is naturally defined in levels. The level is the
integral of the growth rates, of course, and growth rates make it a
little easier to focus, at least implicitly, on how the output gap is
likely to change over time.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Basu and Fernald
tance of economic weakness in reducing inflationary pressures.25 Moreover, a discussion of the
issue highlights some of what we know, and do
not know, about potential output. Some of the
considerations are closely linked to earlier points
we have made, but these considerations also
allow a discussion of other issues that are not
included in the simple models discussed here.
Several arguments suggest that potential
output growth might currently be running at a
relatively rapid pace. First, and perhaps most
importantly, TFP growth has been relatively rapid
from the end of 2006 through the third quarter
of 2008 (see Table 2). During this period output
growth itself was relatively weak, and hours per
worker were generally falling; hence, following
the logic in Basu, Fernald, and Kimball (2006),
factor utilization appears to have been falling as
well. As a result, in both the consumption and
the investment sectors, utilization-adjusted TFP
(from Fernald, 2008) has grown at a more rapid
pace than its post-1995 average. This fast pace has
occurred despite the reallocations of resources
away from housing and finance and the high level
of financial stress.
Second, substantial declines in wealth are
likely to increase desired labor supply. Most
obviously, housing wealth has fallen and stock
market values have plunged; but tax and expenditure policies aimed at stabilizing the economy
could also suggest a higher present value of taxes.
Declining wealth has a direct, positive effect on
labor supply. In addition, as the logic of Campbell
and Hercowitz (2006) would imply, rising financial stress could lead to increases in labor supply
as workers need to acquire larger down payments
for purchases of consumer durables. And if there
is habit persistence in consumption, workers
might also seek, at least temporarily, to work more
hours to smooth the effects of shocks to gasoline
and food prices.
Nevertheless, there are also reasons to be concerned that potential output growth is currently
lower than its pace over the past decade or so.
First, Phelps (2008) raises the possibility that
because of a sectoral shift away from housingrelated activities and finance, potential output
growth is temporarily low and the natural rate of
unemployment is temporarily high. Although
qualitatively suggestive, it is unclear that the sectoral shifts argument is quantitatively important.
For example, Valletta and Cleary (2008) look at
the (weighted) dispersion of employment growth
across industries, a measure used by Lilien (1982).
They find that as of the third quarter of 2008, “the
degree of sectoral reallocation…remains low relative to past economic downturns.” Valletta and
Cleary (2008) also consider job vacancy data,
which Abraham and Katz (1986) suggest could
help distinguish between sectoral shifts and pure
cyclical increases in unemployment and employment dispersion. The basic logic is that in a sectoral shifts story, expanding firms should have
high vacancies that partially or completely offset
the low vacancies in contracting firms. Valletta
and Cleary find that the vacancy rate has been
steadily falling since late 2006.26
Third, Bloom (2008) argues that uncertainty
shocks are likely to lead to a sharp decline in output. As he puts it, there has been “a huge surge in
uncertainty that is generating a rapid slow-down
in activity, a collapse of banking preventing many
of the few remaining firms and consumers that
want to invest from doing so, and a shift in the
political landscape locking in the damage through
protectionism and anti-competitive policies”
(p. 4). His argument is based on the model simulations in Bloom (2007), in which an increase in
macro uncertainty causes firms to temporarily
pause investment and hiring. In his model, productivity growth also falls temporarily because
of reduced reallocation from lower- to higherproductivity establishments.
Fourth, the credit freeze could directly reduce
productivity-improving reallocations, along the
lines suggested by Bloom (2007), as well as Eisfeldt
and Rampini (2006). Eisfeldt and Rampini argue
that, empirically, capital reallocation is procycli-
25
26
For example, in the minutes from the September 2008 FOMC
meeting, participants forecast that over time “increased economic
slack would tend to damp inflation” (Board of Governors, 2008).
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Valletta and Cleary do find some evidence that the U.S. Beveridge
curve might have shifted out in recent quarters relative to its position from 2000 to 2006.
J U LY / A U G U S T
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203
Basu and Fernald
cal, whereas the benefits (reflecting cross-sectional
dispersion of marginal products) are countercyclical. These observations suggest that the
informational and contractual frictions, including
financing constraints, are higher in recessions.
The situation as of late 2008 is one in which
financing constraints are particularly severe,
which is likely to reduce efficient reallocations
of both capital and labor.
Fifth, there could be other effects from the
seize-up of financial markets in 2008. Financial
intermediation is an important intermediate input
into production in all sectors. If it is complementary with other inputs (as in Jones, 2008), for
example, you need access to the commercial
paper market to finance working capital needs—
then it could lead to substantial disruptions of
real operations.
Finally, the substantial volatility in commodity prices, especially oil, in recent years could
affect potential output. That said, although oil is
a crucial intermediate input into production,
changes in oil prices do not have a clear-cut effect
on TFP, measured as domestic value added relative to primary inputs of capital and labor. They
might, nevertheless, influence equilibrium output
by affecting equilibrium labor supply. Blanchard
and Galí (2007) and Bodenstein, Erceg, and
Guerrieri (2008), however, are two recent analyses
in which, because of (standard) separable preferences, there is no effect on flexible price GDP or
employment from changes in oil prices. So there
is no a priori reason to expect fluctuations in oil
prices to have a substantial effect on the level or
growth rate of potential output.
A difficulty for all these arguments that potential output growth might be temporarily low is
the observation already made, that productivity
growth (especially after adjusting for utilization)
has, in fact, been relatively rapid over the past
seven quarters.
It is possible the productivity data have been
27
Note also that the data are all subject to revision. For example, the
annual revision in 2009 will revise data from 2006 forward. In addition, labor-productivity data for the nonfinancial corporate sector,
which is based on income-side rather than expenditure-side data,
show less of a slowdown in 2005 and 2006 and less of a pickup
since then. That said, even the nonfinancial corporate productivity
numbers have remained relatively strong in the past few years.
204
J U LY / A U G U S T
2009
mismeasured in recent quarters.27 Basu, Fernald,
and Shapiro (2001) highlight variations in disruption costs associated with tangible investment.
Comparing 2004:Q4–2006:Q4 (when productivity
growth was weak) with 2006:Q4–2008:Q3 (when
productivity was strong), growth in business fixed
investment was very similar, suggesting that timevarying disruption costs probably explain little of
the recent variation in productivity growth rates.
Basu et al. (2004) and Oliner, Sichel, and
Stiroh (2007) discuss the role of mismeasurement
associated with intangible investments, such as
organizational changes associated with IT. With
greater concerns about credit and cash flow, firms
might have deferred organizational investments
and reallocations; in the short run, such deferral
would imply faster measured productivity growth,
even if true productivity growth (in terms of total
output, the sum of measured output plus unobserved intangible investment) were constant. Basu
et al. (2004) argue for a link between observed
investments in computer equipment and unobserved intangible investments in organizational
change. Growth in computer and software investment does not show a notable difference between
the 2004:Q4–2006:Q4 and 2006:Q4–2008:Q3
periods. If anything, the investment rate was
higher in the latter period—so that this proxy
again does not imply mismeasurement.
Given wealth effects on labor supply and
strong recent productivity performance—along
with the failure of typical proxies for mismeasurement to explain the productivity performance—
there are reasons for optimism about the short-run
pace of potential output growth. Nevertheless, the
major effects of the adverse shocks on potential
output seem likely to be ahead of us. For example,
the widespread seize-up of financial markets has
been especially pronounced only in the second
half of 2008. We expect that as the effects of the
collapse in financial intermediation, the surge in
uncertainty, and the resulting declines in factor
reallocation play out over the next several years,
short-run potential output growth will be constrained relative to where it otherwise would
have been.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Basu and Fernald
CONCLUSION
Basu, Susanto and Fernald, John G. “Returns to Scale
in U.S. Production: Estimates and Implications.”
Journal of Political Economy, April 1997, 105(2),
pp. 249-83.
This article has highlighted a few things we
think we know about potential output—namely,
the importance in both the short run and the long
run of rapid technological change in producing
equipment investment goods and the likely time
variation in the short-run growth rate of potential.
Our discussion of these points has, of course,
pointed toward some of the many things we do
not know.
Taking a step back, we have advocated thinking about policy in the context of explicit models
that suggest ways to think about the world economy, including potential output. But there is an
important interplay between theory and measurement, as the discussion suggests. Every day, policymakers grapple with challenges that are not
present in the standard models. Not only do they
not know the true model of the economy, they also
do not know the current state variables or the
shocks with any precision; and the environment
is potentially nonstationary, with the continuing
question of whether structural change (e.g., parameter drift) has occurred. Theory (and practical
experience) tells us that our measurements are
imperfect, particularly in real time. Not surprisingly, central bankers look at many of the real-time
indicators and filter them analytically—relying
on theory and experience. Estimating potential
output growth is one modest and relatively transparent example of this interplay between theory
and measurement.
Basu, Susanto; Fernald, John G.; Oulton, Nicholas
and Srinivasan, Sylaja. “The Case of the Missing
Productivity Growth: Or, Does Information
Technology Explain Why Productivity Accelerated
in the United States but Not the United Kingdom?”
in M. Gertler and K. Rogoff, eds., NBER
Macroeconomics Annual 2003. Cambridge, MA:
MIT Press, 2004, pp. 9-63.
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F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Basu and Fernald
APPENDIX
A SIMPLE TWO-SECTOR STICKY PRICE MODEL
28
Households
The economy is populated by a representative household which maximizes its lifetime utility,
denoted as
∞
maxE 0 ∑u (Ct , Lt ),
t =0
where Ct is consumption of a constant elasticity of substitution basket of differentiated varieties
ξ
ξ −1
 1
 ξ −1
Ct =  ∫ C ( z ) ξ dz 
0


and Lt is labor effort. u, the period felicity function, takes the following form:
ut = lnCt −
Lηt +1
,
η+1
where η is the inverse of the Frisch elasticity of labor supply. The maximization problem is subject to
several constraints. The flow budget constraint, in nominal terms, is the following:
Bt + PtI I t + PtC Ct = Wt Lt + Rt K t −1 + (1 + it −1 ) Bt −1 + ∆,
ξ
ξ −1
 1
 ξ −1
I =  ∫ I (z ) ξ dz  .
0


where
The price indices are defined as follows:
PtC
I
=
Pt =
( ∫ (z ) dz )
( ∫ P (z ) dz )
1 C
P
0 t
1 I
0 t
1−ξ
1−ξ
1
1−ξ
1
1−ξ
.
Moreover,
(A1)
K t = I t + (1 − δ ) K t −1
(A2)
Lt = LCt + LIt
(A3)
K t −1 = K tC + K tI .
28
The appendix was written primarily by Alessandro Barattieri.
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
J U LY / A U G U S T
2009
209
Basu and Fernald
Notice that total capital is predetermined, while sector-specific capital is free to move in each
period. To solve the problem, we write the Lagrangian as
L = lnCt −
Lηt +1
+ ... − Λt Bt + PtI I t + PtC Ct − Wt Lt − Rt Kt −1 − (1 + it −1 ) Bt −1 − ∆t
η+1
(
(
)
)
− β Et Λt +1 Bt +1 + PtI+1I t +1 + PtC+1Ct +1 − Wt +1Lt +1 − Rt +1K t − (1 + it ) Bt − ∆t +1 − ...
The first-order conditions of the maximization problem for consumption, nominal bond, labor,
and capital are as follows:
1
= PtC Λt
(A4)
Ct
(A5)
Λt = β E t (1 + it ) Λt +1 
(A6)
Lη = Λtw t
(A7)
Λt PtI = β E t  Λt +1 Rt +1 + PtI+1 (1 − δ )  .
(
)
Table A1 provides baseline calibrations for all parameters.
Table A1
Baseline Calibration
Parameter
Value
Parameter
Value
β
0.99
INV_SHARE
η
0.25
C_SHARE
0.8
αC
0.3
LI/L
0.2
αI
0.3
LC/L
0.8
δ
0.025
KI/K
0.2
ΓC
1.1
KC/K
0.8
I
Γ
1.1
ρi
0.8
θC
0.75
φπ
1.5
θI
0.75
φµ
0.5
(1 − θC ) (1 − βθC )
ρC
0.99
θC
ρI
0.99
σεtC
1
(1 − θ I ) (1 − βθ I )
σεtI
1
σvt
1
ζC
ζI
210
θI
J U LY / A U G U S T
2009
0.2
F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
Basu and Fernald
Firms
Both sectors are characterized by a unitary mass of atomistic monopolistically competitive firms.
Production functions are Cobb-Douglas (possibly with different factor intensities). Productivity in
the two sectors is represented by two AR(1) processes. The cost minimization problem for the firms z
operating in the consumption and investment sectors can be expressed, in nominal terms, as
Min Wt LCt ( z ) + Rt K tC ( z )
(
s.t. YtC (z ) = AtC K tC (z )
αC
) (L
C
t
1−α C
(z ))
− ΦC
and analogously as
Min Wt LIt ( z ) + Rt K tI ( z )
(
s.t. I t = AtI K tI (z )
αI
1−α I
) ( L ( z ))
I
t
− ΦI .
Calling µi with i = C,I the multiplier attached to the minimization problem, reflecting nominal marginal
cost, we can express the factor demand as follows, where we omit z assuming a symmetric equilibrium:
αC
Wt
= (1 − α ) AtC K tC
C
µt
C
C −α
t
( ) (L )
α C −1
Rt
= α AtC K tC
C
µt
( )
Wt
= (1 − α ) AtI K tI
µtI
C
C 1−α
t
(L )
αI
I
I −α
t
( ) (L )
Rt
= α AtI K tI
µtI
α I −1
1−α I
( ) ( )
LIt
.
Taking the ratio for each sector, we get
(A8)
K tC
α Wt
=
1 − α Rt
LCt
(A9)
K tI
α Wt
.
=
1 − α Rt
LIt
Inflation rates are naturally defined as
Πtj =
(A10)
Pt j
.
Pt j−1
Finally, given the Cobb-Douglas assumption, it is possible to express the nominal marginal cost as
follows:
(A11)
MC j =
1 1
R αW 1−α Y j + Φ j ,
A j f (α )
(
)
with j = C, I.
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We introduce nominal rigidities through standard Calvo (1983) pricing. Instead of writing the rather
complex equations for the price levels in the C and I sectors, we jump directly to the log-linearized Calvo
equations for the evolution of inflation rates, equations (25) and (26) below.
Monetary Policy
Monetary policy is conducted through a Taylor-type rule with a smoothing parameter and reaction to
inflation and marginal cost. Again, we write the Taylor rule directly in log-linearized form, as equation
(A32) below.
Equilibrium
Beyond the factor market–clearing conditions already expressed, equilibrium also requires a bond
market–clearing condition (B = 0), a consumption goods market–clearing condition (Y C = C ), and an
aggregate adding-up condition (C + I = Y ). (By Walras’s law, we drop the investment market–clearing
condition.)
The Linearized Model
The equations of the model linearized around its nonstochastic steady state are represented by
equations (A12) through (A36), which are 25 equations for the 25 unknown endogenous variables, c,
l I, l C, l, kC, k I, k, λ, w, wC, r, i, yC, I, y, pI, pC, π, π C, π I, µ, µ I, µC, aC, a I, as follows:
(A12)
kt = δ I t + (1 − δ ) kt −1
(A13)
LI I LC C
l +
l = lt
L t
L t
(A14)
K I I KC C
k +
k = kt −1
K t
K t
(A15)
−ct = λt + ptC
(A16)
λt = it + λt +1
(A17)
ηl = λt + w t
(A18)
λt + ptI = λt +1 + 1 − β (1 − δ ) rt +1 + β (1 − δ ) ptI+1
(A19)
y tC = ΓC atC + α C ktC + 1 − α C ltC
(A20)
I t = Γ I atI + α I ktI + 1 − α I ltI
(A21)
ktC + rt = w t + ltC
(A22)
ktI + rt = w t + ltI
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F E D E R A L R E S E R V E B A N K O F S T . LO U I S R E V I E W
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(A23)
µtC = α rt + (1 − α )w t − atC
(A24)
µtI = α rt + (1 − α )w t − atI
(A25)
π tC = βπtC+1 + ζ µtC − p C
(A26)
π tI = βπtI+1 + ζ µtI − p I
(A27)
π tC = ptC − ptC−1
(A28)
π tI = ptC − ptI−1
(A29)
µt = C_share ⋅µtC + INV_share ⋅µtI
(A30)
π t = C_share ⋅π tC + INV_share ⋅π tI
(A31)
w tC = w t − ptC
(A32)
it = ρi it −1 + (1 − ρi ) φπ πt + φµ µt
(A33)
y t = C_share ⋅ct + INV_share ⋅I t
(A34)
y tC = ct
(A35)
atC = ρC atC−1 + εtC
(A36)
atI = ρI atI−1 + εtI .
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